I confess to never having been a big fan of the "Garden of Eden" plot either...
The primary obstacle to me was the remembrance of the sword of fire that guards the entrance to Eden. However, I had misread the passage...I believed that it would strike down anybody who happened upon the entrance.
When I started doing research, it became clear that that's not necessarily the case.
The idea is growing on me as well, but there are still a few issues that would need to be worked out.
First of all, searching for the Garden of Eden doesn't exactly fall into the traditional notion of archaeology (unless it needs to be excavated for some reason.) Of course, Temple of Doom didn't really involve traditional aracheaology either. This would could fall either way.
While it's true that there doesn't necessarily have to be an opponent, (other than the spectre of the Grim Reaper chasing Indy?), I believe that there must be somebody else also seeking the Garden, and that they will probably be unfriendly to Indy. If so...who?
Finally, I still feel it's important to emphasize that the ending has to end on a positive note, or it will tarnish the series. Despite what may be dramatically exciting for us as fans, the movies also have to appeal to a mainstream audience. There will be redemption for Indy (as there are in each of his movies), but don't expect an ambiguous death. The last thing you want to do is alienate your audience in the final chapter of your series.
A thought...could Indy be seeking the Tree of Life to try and preserve the life of his ailing father?
And if so, does this mean that we're going with the theory that the "Everlasting Life" granted by the Holy Grail was lost when the "Great Seal" clause of the contract was invoked?